Question

The graph of h(x) = x² was transformed to create the graph of k(x) = -1/7x²? Which of these describes the transformation from the graph of h to the graph of k?

A.) A reflection over the x-axls and a vertical stretch
B.) A reflection over the x-axis and a vertical compression
C.) A reflection over the y-axis and a vertical compression
D.) A reflection over the y-axis and a vertical stretch

Answer 1

Given:

The functions are:

`h(x)=x^2`

`k(x)=-(1)/(7)x^2`

To find:

The transformation from the graph of h to the graph of k.

Solution:

The transformation is defined as

`k(x)=ah(x+a)=` .... (1)

Where, a is stretch factor

If 0<|a|<1, then the graph compressed vertically by factor |a| and if |a|>1, then the graph stretch vertically by factor |a|.

If
`a<0`, then the graph of h(x) reflected across the x-axis.

We have,

`h(x)=x^2`

`k(x)=-(1)/(7)x^2`

It can be written as

`k(x)=-(1)/(7)h(x)` ...(2)

On comparing (1) and (2), we get

`a=-(1)/(7)<0`

The graph of h(x) reflected across the x-axis.

`|a|=(1)/(7)<1`

So, the graph is compressed vertically.

It means the graph of h reflection over the x-axls and a vertical stretch to get the graph of k.

Therefore, the correct option is B.